N=1 Supersymmetric Theory of Higher Spin Gauge Fields in AdS(5) at the Cubic Level

TL;DR

This paper constructs a gauge-invariant cubic action for ${\cal N}=1$ higher spin fields in $AdS_5$, including both bosonic and tensor-spinor sectors, by employing the $5d$ HS superalgebra $cu(1,1|8)$ and its reduced quotient $hu_0(1,1|8)$. Using a compensator-based framework and a carefully designed bilinear form, the authors enforce factorization, extra-field decoupling, and $C$-invariance to fix the cubic couplings and demonstrate their invariance under a deformed HS gauge symmetry at the first nontrivial order; the gravitational coupling is encoded in an overall normalization $\Phi_0$. The analysis relies on the First On-Mass-Shell Theorem to reduce the verification to Weyl tensors, and it provides explicit expressions for the bosonic and fermionic coefficients ensuring consistency of the free and cubic interactions in $AdS_5$. While the results establish cubic-level consistency for both unreduced and reduced spectra, a full nonlinear completion and extensions to ${\cal N}\ge 2$ remain challenging due to the need for mixed-symmetry fields and potential superspace formulations. The work sets a foundation for exploring AdS/CFT dualities in five-dimensional higher spin contexts and guides future generalizations to higher orders and extended supersymmetries.

Abstract

We formulate gauge invariant interactions of totally symmetric tensor and tensor-spinor higher spin gauge fields in AdS(5) that properly account for higher-spin-gravitational interactions at the action level in the first nontrivial order.